# Towards Trustworthy Vital Sign Forecasting: Leveraging Uncertainty for Prediction Intervals

arXiv: https://arxiv.org/abs/2509.01319 · HTML: https://mlsanity.com/paper/2509.01319/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 71 references that are in the map.
- First posted on arXiv 1 Sep 2025.

## Builds on (most cited first, 26 of 26)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts](https://mlsanity.com/paper/2006.09239/) (2020)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Masksembles for Uncertainty Estimation](https://mlsanity.com/paper/2012.08334/) (2020)
- [Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimation](https://mlsanity.com/paper/2110.03051/) (2021)
- [On the Practicality of Deterministic Epistemic Uncertainty](https://mlsanity.com/paper/2107.00649/) (2021)
- [Conformal prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [GradDiv: Adversarial Robustness of Randomized Neural Networks via Gradient Diversity Regularization](https://mlsanity.com/paper/2107.02425/) (2021)
- [Distance-based Confidence Score for Neural Network Classifiers](https://mlsanity.com/paper/1709.09844/) (2017)
- [Training-Free Uncertainty Estimation for Dense Regression: Sensitivity as a Surrogate](https://mlsanity.com/paper/1910.04858/) (2019)
- [Adaptive Bounding Box Uncertainties via Two-Step Conformal Prediction](https://mlsanity.com/paper/2403.07263/) (2024)
- [Multivariate Conformal Prediction using Optimal Transport](https://mlsanity.com/paper/2502.03609/) (2025)
- [A Transformer-based Diffusion Probabilistic Model for Heart Rate and Blood Pressure Forecasting in Intensive Care Unit](https://mlsanity.com/paper/2301.06625/) (2023)
- [Weighted Aggregation of Conformity Scores for Classification](https://mlsanity.com/paper/2407.10230/) (2024)
- [Conformal Prediction for Stochastic Decision-Making of PV Power in Electricity Markets](https://mlsanity.com/paper/2403.20149/) (2024)
- [Training, Architecture, and Prior for Deterministic Uncertainty Methods](https://mlsanity.com/paper/2303.05796/) (2023)
- [Discretization-Induced Dirichlet Posterior for Robust Uncertainty Quantification on Regression](https://mlsanity.com/paper/2308.09065/) (2023)
- [Graph-enabled Reinforcement Learning for Time Series Forecasting with Adaptive Intelligence](https://mlsanity.com/paper/2309.10186/) (2023)
- [Flow-based Conformal Prediction for Multi-dimensional Time Series](https://mlsanity.com/paper/2502.05709/) (2025)
- [TFT-multi: simultaneous forecasting of vital sign trajectories in the ICU](https://mlsanity.com/paper/2409.15586/) (2024)
- [A Rate-Distortion View of Uncertainty Quantification](https://mlsanity.com/paper/2406.10775/) (2024)

## Built on by (most cited first, 2 of 2)

- [Robust Uncertainty Estimation under Distribution Shift via Difference Reconstruction](https://mlsanity.com/paper/2601.19341/) (2026)
- [Explainable Uncertainty Estimation for Reliable Medical AI](https://mlsanity.com/paper/2608.28052/) (2026)

## Abstract (arXiv)

Vital signs, such as heart rate and blood pressure, are critical indicators of patient health and are widely used in clinical monitoring and decision-making. While deep learning models have shown promise in forecasting these signals, their deployment in healthcare remains limited in part because clinicians must be able to trust and interpret model outputs. Without reliable uncertainty quantification -- particularly calibrated prediction intervals (PIs) -- it is unclear whether a forecasted abnormality constitutes a meaningful warning or merely reflects model noise, hindering clinical decision-making. To address this, we present two methods for deriving PIs from the Reconstruction Uncertainty Estimate (RUE), an uncertainty measure well-suited to vital-sign forecasting due to its sensitivity to data shifts and support for label-free calibration. Our parametric approach assumes that prediction errors and uncertainty estimates follow a Gaussian copula distribution, enabling closed-form PI computation. Our non-parametric approach, based on k-nearest neighbours (KNN), empirically estimates the conditional error distribution using similar validation instances. We evaluate these methods on two large public datasets with minute- and hour-level sampling, representing high- and low-frequency health signals. Experiments demonstrate that the Gaussian copula method consistently outperforms conformal prediction baselines on low-frequency data, while the KNN approach performs best on high-frequency data. These results underscore the clinical promise of RUE-derived PIs for delivering interpretable, uncertainty-aware vital sign forecasts.